Correct Answer - Option 3 : A and D
Given:
Average score in 11 innings = 70
Average score in 10 innings = 64
Formula Used:
Average = Sum of values/Number of values
Calculation:
Sum of score in 10 innings = Average score in 10 innings × Number of innings
⇒ Sum of score in 10 innings = 64 × 10
⇒ Sum of score in 10 innings = 640
Sum of score in 11 innings = Average score in 11 innings × Number of innings
⇒ Sum of score in 11 innings = 70 × 11
⇒ Sum of score in 11 innings = 770
Sum of score in 10 innings + Score in 11th inning = 770
⇒ 640 + S = 770
⇒ S = 130
Checking options:
A. S/2 > 64
130/2 = 65
⇒ 65 > 64
⇒ A is correct.
B. S < 110
130 > 110
⇒ B is not correct.
C. 64 < S < 70
130 > 70
⇒ C is not correct
D. 200 < 2S < 300
2S = 260
⇒ 200 < 260 < 300
⇒ D is correct.
∴ A and D are correct